Generally, an absolute distance meter (ADM) is a device that determines the distance to a remote target. It does this by sending laser light to the target and then collecting light that the target reflects or scatters. An ADM may be used to measure distances in one dimension or it may be attached into a more complex device having the ability to measure quantities corresponding to additional dimensions (degrees of freedom).
An example of such a device is a laser tracker, which measures three-dimensional spatial coordinates. The laser tracker sends a laser beam to a retroreflector target that is held against a surface of interest or placed into a fixed nest. The most common type of retroreflector target is the spherically mounted retroreflector (SMR), which may comprise a cube-corner retroreflector mounted within a sphere with the vertex of the cube-corner at the sphere center.
A gimbal mechanism within the laser tracker may be used to direct a laser beam from the tracker to the SMR. Part of the light retroreflected by the SMR enters the laser tracker and passes onto a position detector. A control system within the laser tracker can use the position of the light on the position detector to adjust the rotation angles of the mechanical azimuth and zenith axes of the laser tracker to keep the laser beam centered on the SMR. In this way, the tracker is able to track an SMR that is moved over the surface of an object of interest.
Part of the light retroreflected into the laser tracker may also be passed into a distance-measuring device (distance meter) such as an interferometer or ADM. Angular encoders attached to the mechanical azimuth and zenith axes of the tracker may also measure the azimuth and zenith angles of the laser beam (with respect to the tracker frame of reference). The one distance measurement and two angle measurements performed by the laser tracker are sufficient to completely specify the three-dimensional location of the SMR.
A general comparison of interferometric distance measuring and absolute distance measurement follows. In the laser tracker, an interferometer (if present) may determine the distance from a starting point to a finishing point by counting the number of increments of known length (usually the half-wavelength of the laser light) that pass as a retroreflector target is moved between the two points. If the beam is broken during the measurement, the number of counts cannot be accurately known, causing the distance information to be lost. By comparison, the ADM in a laser tracker determines the absolute distance to a retroreflector target without regard to beam breaks. Because of this, the ADM is said to be capable of “point-and-shoot” measurement.
Although there are several sources of error in an interferometer measurement, in most cases the dominant error is in the value of the average wavelength of the laser light over its path through the air. The wavelength at a point in space is equal to the vacuum wavelength of the laser light divided by the index of refraction of the air at that point. The vacuum wavelength of the laser is usually known to high accuracy (better than one part in 10,000,000), but the average refractive index of air is known less accurately. The refractive index of air is found by first using sensors to measure the temperature, pressure, and humidity of the air and then inserting these measured values into an appropriate equation, such as the Ciddor equation or the Edlin equation.
However, the temperature, pressure, and humidity are not uniform over space, and neither are the sensors perfectly accurate. For example, an error in the average temperature of one degree Celsius causes an error in the refractive index of about one part per million (ppm). As mentioned above, the wavelength of light in air is inversely proportional to the air refractive index.
Similarly, in an ADM, the so-called ADM wavelength (also known as the ambiguity range) is inversely proportional to the air refractive index. Because of this similarity, errors in measuring temperature, pressure, and humidity cause errors in calculated distance that are approximately equal for ADM and interferometer systems.
However, ADMs are prone to errors not found in interferometers. To measure distance, an interferometer uses an electrical counter to keep track of the number of times that two beams of light have gone in and out of phase. The counter is a digital device that does not have to respond to small analog differences. By comparison, ADMs are usually required to measure analog values, such as phase shift or time delay, to high precision.
To understand the difficulties faced by ADMs, we consider three common ADM architectures: the electrical-reference architecture, the optical-reference architecture, and the optical-mixing architecture. In most high-performance ADMs, laser light is modulated, either by applying an electrical signal to the laser source or by sending the laser light through an external modulator such as an acousto-optic modulator or electro-optic modulator. This laser light is sent out of the ADM to a remote target, which might be a retroreflector or a diffuse surface. Light reflects or scatters off the remote target and passes, at least in part, back into the ADM.
Systems based on the optical-mixing architecture are usually called coherent systems. In these systems, the returning laser light is mixed with laser light from another location before being sent to an optical detector that converts the light into an electrical signal. This electrical signal is then decoded to determine the distance from the ADM to the remote target.
Systems that are not coherent are based on one of the other two architectures. In the electrical-reference architecture, the electrical signal from the optical detector is directly compared to the electrical modulation signal applied to the laser or external modulator. In the optical-reference architecture, the electrical signal from the optical detector is compared to the electrical signal output from a second optical detector in the so-called reference channel. In this architecture, modulated laser light is provided to two parallel channels: a measurement channel whose light passes to the remote target and a reference channel whose light stays near the ADM. The reference and measurement channels contain substantially similar elements: similar optics, similar detectors, and similar electronics.
The electrical-reference architecture may suffer from imperfect conversion of electrical modulation into optical modulation. In addition, all three architectures are subject to drift and repeatability errors caused by optical and electrical elements. Optical fibers used in ADM systems, for example, change optical path length with temperature. This problem can be minimized by attempting to match optical fibers in the reference and measurement channels in length and location. Electrical assemblies used in ADM systems, such as amplifiers and filters, cause the modulated signal to undergo a temperature-dependent phase shift. In the optical-reference architecture, this problem can be minimized by attempting to match the temperature-dependent phase shift of the electrical components in the reference and measurement channels. Generally, however, short-term repeatability errors and long-term drift (especially related to changes in ambient temperature) are problematic for ADMs with any architecture. Both short-term repeatability errors and long-term drift errors are examples of a more general category referred to as stability errors.
Laser trackers suffer another kind of error in the measurement of distance regardless of whether the distance meter is an ADM or an interferometer. This type of error is usually referred to an R0 (R-zero) error. In a laser tracker, light is considered to pass through a pivot point, also referred to as a gimbal point. It is desirable to reference all distances measured by an ADM or interferometer to this gimbal point. To do this, a magnetic nest designed to kinematically support the SMR is rigidly attached to the body of the laser tracker. Ordinarily, this nest, which is said to be located at the home position, is attached below the exit aperture of the laser tracker so that it does not block the laser beam during measurements. A procedure, referred to as an R0 compensation, is carried out to determine the R0 distance from the gimbal point to the home position. During the course of measurements, the SMR is occasionally brought to the home position and the distance reset to the R0 distance. For the interferometer, this provides a simple means of recovering from a broken laser beam. For the ADM, it provides a way of removing electrical or thermal drift.
The metal of the tracker housing expands or contracts with temperature, so the R0 value increases or decreases correspondingly. It is possible to correct the R0 value in real time to partially account for this expansion. This is done by embedding one or more temperature sensors within the metal body of the tracker and then using this measured temperature to correct for the thermal expansion of the metal. However, this procedure is not perfect because neither the average temperature of the metal nor the coefficient of thermal expansion of the metal are exactly known. Because the expansion or contraction in R0 is proportional to the product of the length R0, the coefficient of thermal expansion, and the change in temperature, it follows that the magnitude of the error in the corrected R0 measurement increases in direct proportional to the R0 distance. Unfortunately, this R0 distance is necessarily non-zero since the nest at the home position is mounted to the body of the tracker.